A Mathematical Model for a Transmissible Disease with a Variant

A. Otto, Morou Amidou
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引用次数: 1

Abstract

The outbreak of the Coronavirus (COVID-19) pandemic around the world has caused many health and socioeconomic problems, and the identification of variants like Delta and Omicron with similar and often even more transmissible modes of transmission has motivated us to do this study. In this article, we have proposed and analyzed a mathematical model in order to study the effect of health precautions and treatment for a disease transmitted by contact in a constant population. We determined the four equilibria of the system of ordinary differential equations representing the model and characterized their existence using exact methods of algebraic geometry and computer algebra. The model is studied using the stability theory for systems of differential equations and the basic reproduction number R 0 . The stability of the equilibria is analyzed using the Lienard-Chipart criterion and Lyapunov functions. The asymptotic or global stability of endemic equilibria is established, and the disease-free equilibrium is globally asymptotically stable if R 0 < 1 . Model simulation is done with Python software to study the effects of health precautions and treatment, and the results are analyzed. It is observed that if the rate of treatment and compliance with health precautions are high, the number of infections decreases in the classes of infectious and is canceled out over time. It is concluded that the high treatment rate accompanied by a suitable rate of compliance with health precautions allows for the control the disease.
带有变异的传染性疾病的数学模型
全球爆发的冠状病毒(COVID-19)大流行造成了许多健康和社会经济问题,发现Delta和Omicron等具有相似且通常更具传染性的传播模式的变异,促使我们进行这项研究。在本文中,我们提出并分析了一个数学模型,以研究恒定人群中接触传播疾病的卫生预防和治疗效果。我们确定了代表该模型的常微分方程组的四个平衡点,并用代数几何和计算机代数的精确方法表征了它们的存在性。利用微分方程组的稳定性理论和基本再现数r0对模型进行了研究。利用Lienard-Chipart判据和Lyapunov函数分析了平衡点的稳定性。建立了地方病平衡点的渐近稳定性或全局稳定性,当R 0 < 1时,无病平衡点是全局渐近稳定的。利用Python软件对模型进行仿真,研究健康预防和治疗的效果,并对结果进行分析。可以观察到,如果治疗和遵守保健预防措施的比率很高,感染的数量就会减少,并随着时间的推移而被消除。结论认为,高治愈率和适当的卫生预防措施依从率可使疾病得到控制。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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